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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.powers.powm1"></a><a class="link" href="powm1.html" title="powm1">powm1</a>
</h3></div></div></div>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">powm1</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<p>
        namespace boost{ namespace math{
      </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">powm1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">);</span>

<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 22. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&gt;</span>
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">powm1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 22. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&amp;);</span>

<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
        Returns x<sup>y </sup> - 1.
      </p>
<p>
        The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result
        type calculation rules</em></span></a> when T1 and T2 are different types.
      </p>
<p>
        The final <a class="link" href="../../policy.html" title="Chapter 22. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can
        be used to control the behaviour of the function: how it handles errors,
        what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 22. Policies: Controlling Precision, Error Handling etc">policy
        documentation for more details</a>.
      </p>
<p>
        There are two domains where this is useful: when <span class="emphasis"><em>y</em></span> is
        very small, or when <span class="emphasis"><em>x</em></span> is close to 1.
      </p>
<p>
        Note that for invalid input this function may raise a <a class="link" href="../error_handling.html#math_toolkit.error_handling.domain_error">domain_error</a>
        or <a class="link" href="../error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>
        as appropriate.
      </p>
<p>
        Implemented in terms of <code class="computeroutput"><span class="identifier">expm1</span></code>.
      </p>
<p>
        The following graph illustrates the behaviour of powm1:
      </p>
<div class="blockquote"><blockquote class="blockquote"><p>
          <span class="inlinemediaobject"><img src="../../../graphs/powm1.svg" align="middle"></span>

        </p></blockquote></div>
<h5>
<a name="math_toolkit.powers.powm1.h0"></a>
        <span class="phrase"><a name="math_toolkit.powers.powm1.accuracy"></a></span><a class="link" href="powm1.html#math_toolkit.powers.powm1.accuracy">Accuracy</a>
      </h5>
<p>
        Should have approximately 2-3 epsilon accuracy.
      </p>
<div class="table">
<a name="math_toolkit.powers.powm1.table_powm1"></a><p class="title"><b>Table 8.85. Error rates for powm1</b></p>
<div class="table-contents"><table class="table" summary="Error rates for powm1">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> double
                </p>
              </th>
<th>
                <p>
                  GNU C++ version 7.1.0<br> linux<br> long double
                </p>
              </th>
<th>
                <p>
                  Sun compiler version 0x5150<br> Sun Solaris<br> long double
                </p>
              </th>
<th>
                <p>
                  Microsoft Visual C++ version 14.1<br> Win32<br> double
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  powm1
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span>
                </p>
              </td>
<td>
                <p>
                  <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span>
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
<br class="table-break"><h5>
<a name="math_toolkit.powers.powm1.h1"></a>
        <span class="phrase"><a name="math_toolkit.powers.powm1.testing"></a></span><a class="link" href="powm1.html#math_toolkit.powers.powm1.testing">Testing</a>
      </h5>
<p>
        A selection of random high precision test values calculated using NTL::RR
        at 1000-bit precision.
      </p>
</div>
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      Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
      Walker and Xiaogang Zhang<p>
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